A company manufactures two types of lawn mowers: riding mowers and

Question 1
A carpenter makes tables and chairs. Each table can be sold for a profit of $50 and each chair for a profit of $30. The carpenter works a maximum of 40 hours per week and spends 5 hours to make a table and 2 hours to make a chair. Customer demand requires that he makes at least twice as many chairs as tables. The carpenter stores the finished products in his garage, and there is room for a maximum of 6 furniture pieces each week. Determine the carpenter’s optimal production mix? Solve using Graphical method.

Question 2
A company manufactures two types of lawn mowers: riding mowers and push mowers. The company has the option of manufacturing the mowers in-house, or outsourcing the entire operation. In-house manufacturing requires the following four operations: production, assembly, electrical wiring, and final inspection. The following table summarizes the weekly hours of processing time available and the processing time required by each operation.
 

Hours Required per Mower
Riding Mower Push Mower Hours Available
Production 3 1.5 40
Assembly 5 2 30
Electrical Wiring 1 0.5 45
Final Inspection 0.5 0.25 40
 

The company has a weekly demand of 5 riding mowers and 3 push mowers. The company makes its riding mowers in-house for $500 each and its push mower for $200 each. Alternatively, it can outsource its riding and push mowers for $550 and $225 each, respectively. Use linear programming to formulate the problem.